Connection To Ricci Flow
For more details on this relationship, see Ricci flow#Relationship_to_uniformization_and_geometrization.In introducing the Ricci flow, Richard Hamilton showed that the Ricci flow on a closed surface uniformizes the metric (i.e., the flow converges to a constant curvature metric). However, his proof relied on the uniformization theorem. Xiuxiong Chen, Peng Lu, and Gang Tian (2006) showed that it is nevertheless possible to prove the uniformization theorem via Ricci flow.
Read more about this topic: Uniformization Theorem
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